Finding all tangent angles

\tan(\theta+180)=\tan\theta

This means that, if we know one solution for \theta, we can find another by adding 180\degree to that angle.

Negative tangent angles

\tan(-\theta)=-\tan\theta

The tangent of a negative angle is the negative of the tangent of the positive angle

Solving tangent equations

Solve tan\theta=1 for values of \theta between 0\degree and 540\degree.

• \tan^{-1}(1)=45\degree
• 45\degree+180\degree=225\degree
• 225\degree+180\degree=405\degree
• Answer: \theta=45\degree,225\degree,405\degree

Solve tan\theta=-1 for values of \theta between 0\degree and 540\degree.

• \tan^{-1}(-1)=-45\degree
• -45\degree+180\degree=135\degree
• 135\degree+180\degree=315\degree
• 315\degree+180\degree=495\degree
• Answer: \theta=135\degree,315\degree,495\degree

Solve tan\theta=\sqrt{3} for values of \theta between 0\degree and 540\degree.

• \tan^{-1}(\sqrt{3})=60\degree
• 60\degree+180\degree=240\degree
• 240\degree+180\degree=420\degree
• Answer: \theta=60\degree,240\degree,420\degree